Website owner:  James Miller

Prove. Given the function U(x, t) defined for a x b, t > 0. Let the Laplace transform of U(x, t) be

Then the Laplace transform of ∂U²/∂t² is given by

where

Proof. Let V = ∂U/∂t. Then

                                                = s{s L[U] - U(x, 0)} - U_t(x, 0)

                                                = s²u - sU(x, 0) - U_t(x, 0)

Website owner:  James Miller